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Investigation of the $D^{0} \rightarrow K_S^{0} π^{0} η,\ K_S^{0} π^{0} π^0$ decays

Wei Liang, Chu-Wen Xiao, Guo-Mei Gan, Shi-Qi Zhou

Abstract

Inspired by the invariant mass distributions for the decays $D^{0} \rightarrow K_S^{0} π^{0} η$ and $D^{0} \rightarrow K_S^{0} π^{0} π^{0}$ reported by the BESIII Collaboration, we investigate these processes with an unified final state interaction formalism by incorporating both the $S$-wave pseudoscalar meson-pseudoscalar meson interactions within a chiral unitary approach and the $P$-wave contribution from the intermediate resonance $\bar{K}^*(892)$. By performing a combined fit to the invariant mass spectra and taking into account the coherence between the $S$- and $P$-waves, our results are in agreement with the experimental data. For the decay $D^{0} \rightarrow K_S^{0} π^{0} η$, the structure near 1.0 GeV in the $π^0 η$ invariant mass distribution corresponds to the signal of the $a_{0}(980)$, which is dynamically generated from the $S$-wave interactions. In the case of $D^{0} \rightarrow K_S^{0} π^{0} π^{0}$, the near-threshold enhancement in the $π^0π^0$ mass distribution arises from the combined contributions of the $f_0(500)$ and the intermediate $\bar{K}^*(892)$, while the cusp-like structure around 1 GeV$^2$ is associated with the $f_0(980)$.

Investigation of the $D^{0} \rightarrow K_S^{0} π^{0} η,\ K_S^{0} π^{0} π^0$ decays

Abstract

Inspired by the invariant mass distributions for the decays and reported by the BESIII Collaboration, we investigate these processes with an unified final state interaction formalism by incorporating both the -wave pseudoscalar meson-pseudoscalar meson interactions within a chiral unitary approach and the -wave contribution from the intermediate resonance . By performing a combined fit to the invariant mass spectra and taking into account the coherence between the - and -waves, our results are in agreement with the experimental data. For the decay , the structure near 1.0 GeV in the invariant mass distribution corresponds to the signal of the , which is dynamically generated from the -wave interactions. In the case of , the near-threshold enhancement in the mass distribution arises from the combined contributions of the and the intermediate , while the cusp-like structure around 1 GeV is associated with the .
Paper Structure (4 sections, 21 equations, 6 figures, 2 tables)

This paper contains 4 sections, 21 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. results and discussions
  4. Summary

Figures (6)

  • Figure 1: The internal $W$-emission mechanism for the decays $D^{0} \rightarrow K_S^{0} \pi^{0} \eta$ and $D^{0} \rightarrow K_S^{0} \pi^{0} \pi^0$.
  • Figure 2: Diagrammatic representations of rescattering for the decay $D^0 \rightarrow K_S^0 \pi^0 \eta$.
  • Figure 3: Diagrammatic representations of rescattering for the decay $D^0 \rightarrow K_S^0 \pi^0 \pi^0$.
  • Figure 4: Mechanism for the $D^{0} \rightarrow K_S^{0} \pi^{0} \eta$ and $D^{0} \rightarrow K_S^{0} \pi^{0} \pi^0$ decays via the intermediate vector meson $\bar{K}^*(892)$.
  • Figure 5: Combined fit for the invariant mass distributions of the decay $D^0 \rightarrow K_S^0 \pi^0 \eta$. The solid (black) line is the total contributions of the $S$ and $P$ waves, the dash (red) line represents the $S$-wave contributions, the dash-dot (purple) line means the contributions of the $\bar{K}^*(892)$ in the $P$ wave. The dot (black) points are the experimental data measured by the BESIII Collaboration BESIII:2025wmd.
  • ...and 1 more figures